How can I integrate dx / (x^2 - 1)^2 without a substitution?

[aija]

Homework Statement

integrate dx / (x^2 - 1)^2

Homework Equations

The Attempt at a Solution

There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get:

∫( dt / (t-1)^2 * 2sqr(t) )

and it's still impossible to integrate.

 

[arildno]

Try partial fractions decomposition, remembering that (x^2-1)=(x+1)(x-1)

 

[Ray Vickson]

Homework Statement

integrate dx / (x^2 - 1)^2

Homework Equations

The Attempt at a Solution

There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get:

∫( dt / (t-1)^2 * 2sqr(t) )

and it's still impossible to integrate.

A more-or-less standard substitution to try out when you see 'x^2-1' is x = cosh(t).